The full adder makes the operation of addition taking into account an Input-Carry, possibly produced by a previous addition, which makes it ideal for chaining long number additions.

A 4-bit adder makes our life even easier, since 4-bit number addition is very often in digital circuits, and we can use it right-away instead of building it from 4 1-bit adders. As for its shape, well... beaty is in the eye of the beholder.